Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation. Issue 12 (29th October 2021)

• Record Type: Journal Article
• Authors: Gomes, Niladri; Mukherjee, Anirban; Zhang, Feng; Iadecola, Thomas; Wang, Cai‐Zhuang; Ho, Kai‐Ming; Orth, Peter P.; Yao, Yong‐Xin
• Is Part Of: Advanced quantum technologies. Volume 4:Issue 12(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-10-29
• Subjects: quantum algorithms -- quantum chemistry -- quantum computation; Quantum theory -- Periodicals; Quantum computing -- Periodicals; Quantum chemistry -- Periodicals; Quantum electronics -- Periodicals; 537.5
• DOI: 10.1002/qute.202100114
• Languages: English
• ISSNs: 2511-9044

Abstract

Abstract: An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near‐term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan distance is constrained by the quality of the ansatz, the AVQITE method iteratively expands the ansatz along the dynamical path to keep the McLachlan distance below a chosen threshold. This ensures the state is able to follow the quantum imaginary time evolution path in the system Hilbert space rather than in a restricted variational manifold set by a predefined fixed ansatz. AVQITE is used to prepare ground states of H4, H2 O, and BeH2 molecules, where it yields compact variational ansätze and ground state energies within chemical accuracy. Polynomial scaling of circuit depth with system size is shown through a set of AVQITE calculations of quantum spin models. Finally, quantum Lanczos calculations are demonstrated alongside AVQITE without additional quantum resource costs. Abstract : Adaptive variational quantum imaginary time evolution (AVQITE) leads an interacting quantum system from an easy‐to‐prepare reference state to the ground state along an imaginary time path, with an adaptive ansatz which automatically grows initially and saturates, contrasting the linear time growth of the QITE circuit along the same path.